http://www.ck12.org Chapter 4. Triangles and Congruence
First we can see thatm^6 DCA= 15 ◦. This means thatm^6 BAC= 15 ◦also because they are alternate interior angles.
m^6 ABC= 153 ◦was given. This means by the Triangle Sum Theorem thatm^6 BCA= 12 ◦. This means thatm^6 CAD=
12 ◦also because they are alternate interior angles. Finally,m^6 ADC= 153 ◦by the Triangle Sum Theorem.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52621CK-12 Foundation: Chapter4TheThirdAngleTheoremB
Concept Problem Revisited
For two given triangles 4 F GHand 4 XY Z, you were told that^6 F∼=^6 Xand^6 G∼=^6 Y.
By the Third Angle Theorem,^6 H∼=^6 Z.
Vocabulary
Two figures arecongruentif they have exactly the same size and shape. Two triangles arecongruentif the three
corresponding angles and sides are congruent. TheTriangle Sum Theoremstates that the measure of the three
interior angles of any triangle will add up to 180◦. TheThird Angle Theoremstates that if two angles in one triangle
are congruent to two angles in another triangle, then the third pair of angles must also congruent.
Guided Practice
Determine the measure of all the angles in the each triangle.